Claude Berge introduced hypergraphs in 1967 and 1973 as a means to generalize the graph approach. For a graph G = (V, E), a bijection g from V (G) ∪ E(G) into {1, 2,..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic labeling of G if the edge-weights w(xy) = g(x) + g(y), xy ∈ E(G), form an arithmetic progression starting from a and having common difference d. In this paper the concept of Edge Anti – magic labelling in Hyper Graphs are introduced. Some interesting properties of hyper graphs are studied. Investigation of this topic on Crossed prism graph, Cocktail party graph, Complete Tripartite graph are Edge Anti –magic Hyper Graphs has been done.